Answer:
The number of dogs that had both Lyme disease and arthritis is 18
Step-by-step explanation:
Let x represent dogs that have both Lyme disease and arthritis
Dog with only Lyme disease = 42 - x
Dog with only arthritis = 96 - x
The sum of the 3 category should give 120
x + (42 - x) + (96 - x) = 120
Collect like terms and solve
x - x - x + 42 + 96 = 120
-x + 138 = 120
138 - 120 = x
x = 18
Dog with only Lyme disease = 42 - x = 42 - 18 = 24
Dog with only arthritis = 96 - x = 96 - 18 = 78
Therefore, the number of dogs with both Lyme disease and anthritis is 18.
Formula for volume of cylinder is area of base time height
area of base equal pir^2 =3,14*(2,5)^2 = 3,14 *6,25 = 19,625 inches squared
V=area time height
170 = 19,625 *h
h = 170/19,625 = 8,662 inches
Answer:
285 boxes are in the display
Step-by-step explanation:
Given data
top layer box = 1
last row box = 81
to find out
how many box
solution
we know that every row is a square so that if the bottom layer has 81 squares it mean this is 9² and every row has one lesser box
so that next row will have 8^2 and than 7² and so on till 1²
so we can say that cubes in the rows as that
Sum of all Squares = 9² + 8² +..........+ 1²
Sum of Squares positive Consecutive Integers formula are
Sum of Squares of Consecutive Integers = (1/6)(n)(n+1)(2n+1)
here n = 9 so equation will be
Sum of Squares of Consecutive Integers = (1/6) × (9) × (9+1) × (2×9+1)
Sum of Squares of Consecutive Integers = 285
so 285 boxes are in the display
Since the range of the scores given was between 300 and 700 (which is 2 standard deviations below and above the mean), the probability that a randomly selected student's math score - as based on the empirical rule of statistics - is 95%. In decimal form, it is .95.
